Organon (Owen)/Prior Analytics/Book 2

Chap. 1. Recapitulation.—Of the Conclusions of certain Syllogisms.
 * 1.1. Reference to the previous observations. Universal syllogisms infer many conclusions.
 * 1.2. So also do particular affirmative, but not the negative particular.
 * 1.3. Difference between universals of the first and those of the second figure.

Chap. 2. On a true Conclusion deduced from false Premises in the first Figure.
 * 2.1. Material truth or falsity of propositions, is not shared by the conclusion.
 * 2.2. We may infer the true from false premises, but not the false from true premises. Proof—(Vide Aldrich general rules of syllogism.)
 * 2.3. Instance of a false proposition.
 * 2.4. When the major is wholly false, but the minor is true, the conclusion is false; but when the whole is not false, the conclusion is true.
 * 1. Affirmative
 * 2. Negative
 * 2.5. If the major is true wholly, but the minor wholly false, the conclusion is true.
 * 1. Affirmative
 * 2. Negative
 * 2.6. In particulars with a major false, but a minor true, there may be a true conclusion.
 * 1. Affirmative
 * 2. Negative
 * 2.7. If the major is partly false, the conclusion will be true.
 * 1. Affirmative
 * 2. Negative
 * 3. Major true, minor false.
 * 4. Major negative.
 * 5. Major partly, minor wholly, false.
 * 6. Negative.
 * 7. Both false.
 * 8. Major negative.

Chap. 3. The same in the middle Figure.
 * 3.1. In this figure we may infer the true from premises, either one or both wholly or partially false.
 * 1. Universals.
 * 2. One wholly false, the other wholly true.
 * 3. One partly false.
 * 4. Minor or negative.
 * 5. Affirmative partly false.
 * 6. Both partly false.
 * 2. Particulars.
 * 1. Major negative.
 * 2. Major affirmative.
 * 3. Univ. true, part. false.
 * 4. Univ. affirm.
 * 5. Case of both premises false.

Chap. 4. Similar Observations upon a true Conclusion from false Premises in the third Figure.
 * 4.1. The case the same as with the preceding figures.
 * 1. Both univ. affirm.
 * 2. One negative.
 * 3. One partly false.
 * 4. Negatives
 * 5. One wholly false, the other true.
 * 7. Both affirm.
 * 4.2. Particulars follow the same rule, i.e. those with one universal and one particular premise.
 * 4.3. Also negatives.
 * 4.4. If the conclusion is false there must be falsity in one or more of the premises—but this does not hold good vice versâ. Reason of this.

Chap. 5. Of Demonstration in a Circle, in the first Figure.
 * 5.1. Definition of this kind of demonstration—and example.
 * 5.2. A demonstration of this kind not truly made, except through converted terms, and then by assumption "pro concesso," only.
 * 5.3. Case of negatives.
 * 5.4. In particulars the major is not demonstrated, but the minor is.

Chap. 6. Of the same in the second Figure.
 * 6.1. In universals of the second figure an affirmative proposition is not demonstrated.
 * 6.2. But the negative is.
 * 6.3. In particulars the particular proposition alone is demonstrated when the universal is affirmative.

Chap. 7. Of the same in the third Figure.
 * 7.1. In this figure, when both propositions are universal there is no demonstration in a circle.
 * 7.2. There will be demonstration where the minor is universal and the major particular.
 * 7.3. When the affirmative is universal there is demonstration of the particular negative.
 * 7.4. Not when the negative is universal (exception).
 * 7.5. Recapitulation of the preceding chapters.

Chap. 8. Of Conversion of Syllogisms in the first Figure.
 * 8.1. Definition of conversion of syllogism
 * 8.2. Difference whether this is done contradictorily or contrarily. The distinction between these shown.
 * 8.3. In particulars, of the first figure when the conclusion is converted contradictorily both propositions are subverted, if contrarily, neither.

Chap. 9. Of Conversion of Syllogisms in the second Figure.
 * 9.1. In universals we cannot infer the contrary to the major premise, but we may the contradictory—the minor dependent upon the assumption of the conclusion.
 * 9.2. In particulars, if the contrary of the conclusion is assumed, neither proposition is subverted; if the contradictory, both are.

Chap. 10. Of the same in the third Figure.
 * 10.1. In this figure, if the contrary to the conclusion is assumed, neither premise is subverted, but if the contradictory, both.
 * 1. Universals.
 * 10.2. Particulars the same.
 * 10.3. Recapitulation.

Chap. 11. Of Deduction to the Impossible in the first Figure.
 * 11.1. How syllogism is shown, and its distinction from conversion.
 * 11.2. The universal affirm. in the first figure not demonstrable per impossibile.
 * 11.3. But the par. affir. and univ. nega. may be demonstrated, when the contradictory of the conclusion is assumed.
 * 11.4. Also the par. neg. is demonstrated, but if the sub-contrary to the conclusion is assumed, what was proposed is subverted.
 * 11.5. Summary and reason of the above assumption.

Chap. 12. Of the same in the second Figure.
 * 12.1. In the second figure A is proved per absurdum, if the contradictory is assumed, not if the contrary.

Chap. 13. Of the same in the third Figure.
 * 13.1. In this figure both affirmatives and negatives are demonstrable per absurdum.
 * 13.2. Recapitulation.

Chap. 14. Of the difference between the Ostensive, and the Deduction to the Impossible.
 * 14.1. Difference between direct demonstration and that per impossible.
 * 14.2. What is demonstrated per absurdum in the first figure, is proved in the second, ostensively, if the problem be negative, and in the third figure if it be affirmative.
 * 14.3. What is demonstrable per absurdum is so also ostensively and vice versâ.

Chap. 15. Of the Method of concluding from Opposites in the several Figures.
 * 15.1. Of the various figures from which a syllogism is deducible from opposite propositions, the latter of four kinds, (cf. Herm. 7,) but, of three.
 * 15.2. No conclusion from opposites if either kind in the first figure.
 * 15.3. But from both in the second.
 * 15.4. In the third no affirmative is deduced.
 * 15.5. Opposition six-fold
 * 15.6. No true conclusion deducible from such propositions.
 * 15.7. From contradictories a contradiction to the assumption is inferred.
 * 15.8. To infer contradiction in the conclusion, we must have contradiction in the premises. (Vide Whately, b. ii. c. 2 and 3.)

Chap. 16. Of the "Petitio Principii," or Begging the Question.
 * 16.1. What the "petitio principii" is—.
 * 16.2. How this fallacy is effected. See Hill's Logic, p. 331, et seq. Rhet. ii. 24.
 * 2. Example given of mathematicians.
 * 5. Beg the question.
 * 16.3. This fallacy may occur in both the 2nd and 3rd figures, but in the case of an affirmative syllogism by the 3rd and first.

Chap. 17. A Consideration of the Syllogism, in which it is argued, that the false does not happen—"on account of this," ,
 * 17.1. This happens in a deduction to the impossible, which is contradicted not in ostensive demonstration.
 * 17.2. The perfect example of this is when the prop. of which the syllo. consists do not concur.
 * 17.3. Another mode.
 * 17.4. Necessity of connecting the impossible with the terms assumed from the first.
 * 17.5. This not to be employed as if a deduction to the impossible arises from other terms.

Chap. 18. Of false Reasoning.
 * 18.1. False conclusion arises from error in the primary propositions.

Chap. 19. Of the Prevention of a Catasyllogism.
 * 19.1. Rule to prevent the advancement of a catasyllogism is to watch against the same term being twice admitted in the prop.
 * 19.2. Necessity and method of masking our design in argument—two ways of effecting this.

Chap. 20. Of the Elenchus.
 * 20.1. The elenchus (redargutio) is a syllogism of contradiction, to produce which there must be a syllogism—though the latter may subsist without the former (Conf. Sop. Elen. 6.)

Chap. 21. Of Deception, as to Supposition—
 * 21.1. This kind of deception twofold.
 * 21.2. Case of the middles in Barbara and Celarent, not being subaltern.
 * 21.3. Distinction between universal and particular knowledge.
 * 21.4. Our observation of particulars, derived from our knowledge of universals, a peculiarity noticed. (Met. book vi. 9.) Locke's Ess. vi. 4, v. 5, and vi. 2.
 * 21.5. A deception from knowing one prop. and being ignorant of the other.
 * 21.6. Scientific knowledge is predicated triply.
 * 21.7. From a deception of this kind, a person may imagine that a thing concurs with its contrary.

Chap. 22. On the Conversion of the Extremes in the first Figure.
 * 22.1. If the terms connected by a certain middle are converted, the middle must be converted with both.
 * 22.2.
 * 22.3. The mode of converting a negative syllogism, begins from the conclusion, as in Barbara.
 * 22.4. Case of election of opposites.
 * 22.5. The greater good and less evil preferable to the less good and greater evil.
 * 22.6. The desire of the end, the incentive to the pursuit (Eth. b. 1, c. 7.)

Chap. 23. Of Induction.
 * 23.1. Not only dialectic and apodeictic syllogisms, but also rhetorical, and every species of demonstration, are through the above-named figures.
 * 23.2. Induction is proving the major term of the middle by the minor.
 * 23.3. Induction is occurrent in those demonstrations, which are proved without a middle.

Chap. 24. Of Example
 * 24.1., or example, is proving the major of the middle by a term resembling the minor.
 * 24.2.
 * 24.3. Example subsists as part to part, wherein it differs from induction. (Vide note above.)

Chap. 25. Of Abduction.
 * 25.1. a syllogism with a major prem. certain, and the minor more credible than the conclusion.
 * 25.2. Moreover when the minor is proved by the interposition of few middle terms.

Chap. 26. Of Objection.
 * 26.1. (Instantia,) a proposition contrary to a proposition, it differs from a proposition in that it may be either or.
 * 26.2. Method of alleging the.
 * 26.3. Rule for the.
 * 26.4. And for that . Vide note.
 * 26.5. Objection adduced in the first and third figures alone.
 * 26.6. Objections of other kinds to be noticed, vide not. 1, supra; Rhet. ii. 25.

Chap. 27. Of Likelihood, Sign, and Enthymeme.
 * 27.1. consentaneum argumentum, Buhle and Taylor; "verisimile" and "verisimilitudo," Averrois, Waitz; "probablile," Cicero; "likelihood," Sir W. Hamilton;—is a probable proposition.   is a demonstrative proposition, either necessary or probable.  Enthymeme is a syllogism drawn fron either of these.  Cf. Rhet. b. i. c. 2. Soph. Œd. Col. 292 and 1199.
 * 27.2. A sign assumed triply, according to the number of figures.
 * 27.3. If one prop. be enunciated, there is only a sign.
 * 27.4. Syllogism, if it be true, is incontrovertible in the 1st fig., but not so in the last or 2nd fig.
 * 27.5. . (indicium,) a syllogism in the first figure. (Cf. Quintilian, lib. v. c. 9, sec. 8.)
 * 27.6. By the example of physiognomy Aristotle shows that signs especially probable belong to the 1st figure.
 * 27.7. The first physiognomic hypothesis is that natural passion changes at one time the body and soul. The 2nd, that there is one sign of one passion.  The 3rd, that the proper passion of each species of animal may be known.
 * 27.8. Whatever is inferred in this respect is collected in the 1st figure.

